Additive resonances of a controlled van der Pol-Duffing oscillator

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Show simple item record Ji, JC Zhang, N 2010-05-28T09:48:51Z 2008-08-05
dc.identifier.citation Journal of Sound and Vibration, 2008, 315 (1-2), pp. 22 - 33
dc.identifier.issn 0022-460X
dc.identifier.other C1 en_US
dc.description.abstract The trivial equilibrium of a controlled van der Pol-Duffing oscillator with nonlinear feedback control may lose its stability via a non-resonant interaction of two Hopf bifurcations when two critical time delays corresponding to two Hopf bifurcations have the same value. Such an interaction results in a non-resonant bifurcation of co-dimension two. In the vicinity of the non-resonant Hopf bifurcations, the presence of a periodic excitation in the controlled oscillator can induce three types of additive resonances in the forced response, when the frequency of the external excitation and the frequencies of the two Hopf bifurcations satisfy a certain relationship. With the aid of centre manifold theorem and the method of multiple scales, three types of additive resonance responses of the controlled system are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. The amplitudes of the free-oscillation terms are found to admit three solutions; two non-trivial solutions and the trivial solution. Of two non-trivial solutions, one is stable and the trivial solution is unstable. A stable non-trivial solution corresponds to a quasi-periodic motion of the original system. It is also found that the frequency-response curves for three cases of additive resonances are an isolated closed curve. It is shown that the forced response of the oscillator may exhibit quasi-periodic motions on a three-dimensional torus consisting of three frequencies; the frequencies of two bifurcating solutions and the frequency of the excitation. Illustrative examples are given to show the quasi-periodic motions. © 2008 Elsevier Ltd. All rights reserved.
dc.language eng
dc.relation.hasversion Accepted manuscript version en_US
dc.relation.isbasedon 10.1016/j.jsv.2008.01.052
dc.rights NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Sound and Vibration. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Sound and Vibration, [Volume 315, Issues 1–2, 5 August 2008, Pages 22–33 ] en_US
dc.title Additive resonances of a controlled van der Pol-Duffing oscillator
dc.type Journal Article
dc.parent Journal of Sound and Vibration
dc.journal.volume 1-2
dc.journal.volume 315
dc.journal.number 1-2 en_US
dc.publocation London, UK en_US
dc.identifier.startpage 22 en_US
dc.identifier.endpage 33 en_US FEIT.School of Elec, Mech and Mechatronic Systems en_US
dc.conference Verified OK en_US
dc.for 0913 Mechanical Engineering
dc.personcode 950854
dc.personcode 997749
dc.percentage 100 en_US Mechanical Engineering en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US en_US
dc.location.activity en_US
dc.description.keywords en_US
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group /University of Technology Sydney/Faculty of Engineering and Information Technology/School of Elec, Mech and Mechatronic Systems
utslib.copyright.status Open Access 2015-04-15 12:23:47.074767+10

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